“South Korea will be ordering billions of dollars of that equipment, which for them makes a lot of sense and for us it means jobs, reducing our trade deficit with South Korea,” he said.

Moon confirmed the planned purchases which he described as “essential”, saying Seoul had agreed to begin talks to buy US strategic assets to enhance Korea’s defence capabilities.

Under the existing missile pact between the US and the South, Seoul has only been allowed to develop warheads as heavy as 500kg for its missiles.

The US instead offers the South a “nuclear umbrella” against potential attacks, but Seoul has sought to remove the limit in recent years amid the growing missile threat from the North.

The allies had agreed in principle to do so in September following the North’s latest nuclear test, by far its most powerful to date.

Moon, noting “ever-growing threats” from the North’s missiles and nuclear weapons, said Tuesday the two allies had reached a “final agreement” to remove the restriction.

“We also reaffirmed our stance to put maximum pressure and sanctions on the North until it … comes forward for genuine negotiations,” he told reporters.

Trump said: “I think we are making a lot of progress,” adding that President Xi Jinping – whom he has often claimed holds the key to disarming the North – has been “very, very helpful”.

After a relaxed few days in Tokyo, Seoul is a more complicated stop for the mercurial US president.

Trump’s relationship with the liberal-leaning Moon has been cool, and the former property magnate has railed at South Korean moves to engage its neighbour – something he has previously labelled “appeasement”.

But he began his diplomatic day vowing to “figure it all out” with “fine gentleman” Moon, despite their differences on the nuclear-armed North.

As tensions over Pyongyang’s weapons programme have soared, the US president has traded personal insults and threats of war with North Korean leader Kim Jong-un.

Trump arrived from Japan, where he secured Tokyo’s full support for Washington’s stance that “all options are on the table” regarding Pyongyang, and declaring its nuclear ambitions “a threat to the civilised world and international peace and stability”.

He enjoyed three days of near-bromance with Prime Minister Shinzo Abe, calling him “wonderful” after a round of golf and describing US-Japan ties as “really extraordinary”.

But at Camp Humphreys on Tuesday, where US forces stationed in the country have moved their headquarters from downtown Seoul, he and Moon sought a rapprochement.

Three US aircraft carrier strike groups will exercise together in the Western Pacific in the coming days in a show of force rarely seen in the region, US officials said earlier.

“Ultimately, it will all work out” on North Korea, said Trump. “It always works out. It has to work out.”

And Moon – whose parents were evacuated from the North on a US ship during the Korean war – was abundant in his praise for the United States.

“They say one knows a true friend when one is in need,” he told Trump. “The United States is a true friend who has been with us and has bled with us in our time of need.”

South Korea is rolling out the red carpet for Trump as it seeks messages of assurance about the alliance and US resolve.

But while Trump has threatened Pyongyang with “fire and fury”, Moon is mindful that much of Seoul is within range of the North’s artillery and in an address to parliament last week demanded: “There should be no military action on the peninsula without our prior consent.”

Kim Hyun-wook, a professor at the Korea National Diplomatic Academy, said the two allies have “subtle differences in their positions” and underlying suspicions about each other.

South Koreans are divided, with both pro- and anti-Trump demonstrations taking place in downtown Seoul since the weekend, sometimes only a few blocks apart, and a heavy police presence lined the route of his motorcade on Tuesday.

North Korea – which carried out by far its most powerful nuclear test so far in September – itself welcomed Trump to the region with a rhetorical volley via the ruling party’s Rodong newspaper, calling the US a “thrice-cursed nuclear criminal” and condemning “Trump’s mad remarks”.

Another issue on his agenda is commerce between the US and the South, with Trump saying he had “a terrific meeting scheduled on trade” with Moon.

His administration has caused consternation in Seoul by demanding the renegotiation of the five-year-old US-Korea free trade agreement, which Trump has called a “horrible deal” and a “job killer”.

“It will start working out and working out so we create lots of jobs in the United States, which is one of the many important reasons I am here,” Trump said.

On Wednesday, Trump will speak to South Korean MPs but his visit will not include a trip to the demilitarised zone dividing the Korean peninsula, with the administration downplaying the destination as “a little bit of a cliché”.

Some observers have fretted that a gaffe by a president given to off-the-cuff remarks could send tensions rising on the peninsula.

“If Trump says anything that can provoke North Korea, it could send military tensions soaring again,” said professor Koo Kab-woo from the University of North Korean Studies in Seoul.

Additional reporting by Reuters